Collaborative Research: Mechanics of Knots and Tangles of Elastic Rods

合作研究：弹性杆结和缠结的力学

• 批准号: 2101751
• 负责人: Mohammad Khalid Jawed
• 金额: $ 36万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2101751&HistoricalAwards=false
• 关键词: Collaborative; Research; Mechanics; Knots; Tangles

In settings from shipping to sailing to surgery, thousands of different types of knots are used every day, each requiring a specific amount of force to tighten. This force depends on the material properties, friction, and the topology of the knot. A knot typically also has a load-bearing capacity; force beyond this level causes the knot to be undone, and excessive force may result in material failure in the knot. Moreover, some knots hold tight without any external force while others easily get untangled. In other words, the knots can store energy in the material. This concept is called a topological battery with implications in nanometer-sized knots in DNA to macroscopic knots in structural engineering. This award supports research to understand the fundamental science of knots. The work will develop modeling and computational methods for the analysis of the mechanics of knots and tangles. In parallel, it will formulate experimental techniques to systematically study this mechanics. The research will be complemented by developing teaching tools (videos, notes, and demonstrations) for undergraduate and graduate courses. The computational software will also be made publicly available. The research objective of this project is to quantify the mechanical response of knots tied in elastic rods. The project will employ (1) fast numerical simulations inspired by computer graphics, (2) innovative materials with customizable friction, and (3) autonomous robotic experiments to untangle the mechanics of knots. Even in the case of the most basic type of knots (overhand knots), the force required to tie the knot depends on an intricate interplay of (1) elasticity, (2) friction, and (3) topology. Interestingly, the overhand knot may undergo a snap-through buckling instability beyond a critical amount of pull. Such instability in a basic knot points to the richness of the mechanical behavior of knots. After developing simulation and experimental tools, the mechanical response and instabilities of a few common knots, e.g. overhand and shoelace knots, will be investigated. Exploiting the computational speed of the simulation tool and autonomy of robotic experiments, the mechanical response of several types of knots will be quantified to build a library of their mechanics. This data will be used to rationalize the variation of a knot’s mechanical response as a function of the topological, material, and frictional parameters. Similar to the periodic table of elements, a mechanics-based classification scheme of knots will be formulated, where the knots will be grouped into various classes, such as, friction-dominated knots, bending-dominated knots, and others.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

在从航运到帆船再到外科手术的环境中，每天都会使用数千种不同类型的结，每种结都需要特定的力量才能拧紧。该力取决于结点的材料特性、摩擦力和拓扑。结通常也有承重能力；超过这个水平的力会导致结解开，而过大的力可能会导致结中的材料失效。此外，一些结在没有任何外力的情况下紧紧抓住，而另一些很容易解开。换句话说，结可以在材料中储存能量。这一概念被称为拓扑电池，其含义从DNA中的纳米结到结构工程中的宏观结。该奖项支持理解结的基础科学的研究。这项工作将开发用于分析结和缠结的力学的建模和计算方法。同时，它还将制定实验技术，系统地研究这一机制。这项研究将通过为本科生和研究生课程开发教学工具(视频、笔记和演示)来补充。计算软件也将向公众开放。本项目的研究目标是量化弹性杆中结点的力学响应。该项目将采用(1)受计算机图形学启发的快速数值模拟，(2)具有可定制摩擦的创新材料，以及(3)解开结力学的自主机器人实验。即使在最基本的结(上手结)的情况下，打结所需的力也取决于(1)弹性、(2)摩擦和(3)拓扑的复杂相互作用。有趣的是，上手结可能会经历超过临界量拉力的快速屈曲不稳定。基本结的这种不稳定性表明了结的力学行为的丰富性。在开发了模拟和实验工具后，将研究几个常见的结，如上手结和鞋带结的力学响应和不稳定性。利用仿真工具的计算速度和机器人实验的自主性，将量化几种类型的结的力学响应，以建立其力学性能库。这些数据将被用来使结的机械响应作为拓扑、材料和摩擦参数的函数的变化合理化。与元素元素周期表类似，将制定基于力学的结分类方案，其中结将被分成不同的类别，如以摩擦为主的结、以弯曲为主的结等。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Systematic Variation of Friction of Rods

杆摩擦力的系统变化

• DOI: 10.1115/1.4055544
• 发表时间: 2022
• 期刊: Journal of Applied Mechanics
• 作者: Ibrahim Khalil, Md;Tong, Dezhong;Wang, Guanjin;Khalid Jawed, Mohammad;Khoda, Bashir
• 通讯作者: Khoda, Bashir

A Fully Implicit Method for Robust Frictional Contact Handling in Elastic Rods

• DOI: 10.1016/j.eml.2022.101924
• 发表时间: 2022-05
• 期刊: ArXiv
• 作者: Dezhong Tong;Andrew Choi;Jungseock Joo;M. Jawed

Automated Stability Testing of Elastic Rods With Helical Centerlines Using a Robotic System

使用机器人系统对具有螺旋中心线的弹性杆进行自动稳定性测试

• DOI: 10.1109/lra.2021.3138532
• 发表时间: 2022
• 期刊: IEEE Robotics and Automation Letters
• 影响因子: 5.2
• 作者: Tong, Dezhong;Borum, Andy;Jawed, Mohammad Khalid
• 通讯作者: Jawed, Mohammad Khalid

Snap Buckling in Overhand Knots

反手结中的卡扣屈曲

• DOI: 10.1115/1.4056478
• 发表时间: 2023
• 期刊: Journal of Applied Mechanics
• 作者: Tong, Dezhong;Choi, Andrew;Joo, Jungseock;Borum, Andy;Khalid Jawed, Mohammad
• 通讯作者: Khalid Jawed, Mohammad

Ballooning in Spiders using Multiple Silk Threads

• DOI: 10.1103/physreve.105.034401
• 发表时间: 2021-12
• 期刊: Physical review. E
• 作者: C. Habchi;M. Jawed